?(a) Approximate \(f\) by a Taylor polynomial with degree \(n\) at the number \(a\).(b)
Chapter 11, Problem 20(choose chapter or problem)
(a) Approximate \(f\) by a Taylor polynomial with degree \(n\) at the number \(a\).
(b) Use Taylor's Inequality to estimate the accuracy of the approximation \(f(x) \approx T_{n}(x)\) when \(x\) lies in the given interval.
(c) Check your result in part (b) by graphing \(\left|R_{n}(x)\right|\).
\(f(x)=x \ln x, a=1, n=3,0.5 \leqslant x \leqslant 1.5\)
Equation Transcription:
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Text Transcription:
f
n
a
f(x)approxT_n(x)
x
|R_n(x)|
f(x)=x ln x,a=1,n=2,0.5 leqslant x leqslant 1.5
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